Robust finite-time sliding mode synchronization of fractional-order hyper-chaotic systems based on adaptive neural network and disturbances observer

Abstract

In this paper, a novel sliding mode control method based on neural network and disturbances observer is designed to satisfy the synchronization of hyper-chaotic fractional-order systems in finite time. It is completely robust against unknown uncertainties and external disturbances. Compared with existing methods, an adaptive neural network and disturbances observer existing in sliding mode law can lessen the chattering effectively. Numerical simulations are applied to demonstrate the efficiency of the proposed control method.

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References

  1. 1.

    Li C, Chen G (2004) Chaos and hyperchaos in the fractional-order Rössler equations[J]. Phys A Statistic Mech Appl 341:55–61

    Article  Google Scholar 

  2. 2.

    Michalski MW (1993) Derivatives of noninteger order and their applications[M]. Polska Akademia Nauk, Institut Matematyczny, Warszawa

    Google Scholar 

  3. 3.

    Hartley TT, Lorenzo CF, Qammer HK (1995) Chaos in a fractional order Chua’s system[J]. IEEE Trans Circuits Syst I Fundamental Theory Appl 42(8):485–490

    Article  Google Scholar 

  4. 4.

    Magin RL (2006) Fractional calculus in bioengineering[M]. Begell House, Redding

    Google Scholar 

  5. 5.

    Baillieul J, Brockett R, Washburn R (1980) Chaotic motion in nonlinear feedback systems[J]. IEEE Trans Circuits Syst 27(11):990–997

    MathSciNet  Article  Google Scholar 

  6. 6.

    Levant A (1993) Sliding order and sliding accuracy in sliding mode control[J]. Int J Control 58(6):1247–1263

    MathSciNet  Article  Google Scholar 

  7. 7.

    Wang XY, Song JM (2009) Synchronization of the fractional order hyperchaos Lorenz systems with activation feedback control[J]. Commun Nonlinear Sci Numer Simul 14(8):3351–3357

    Article  Google Scholar 

  8. 8.

    Wen G, Xu D (2005) Nonlinear observer control for full-state projective synchronization in chaotic continuous-time systems[J]. Chaos Solitons Fractals 26(1):71–77

    Article  Google Scholar 

  9. 9.

    Landau ID, Lozano R, M’Saad M (1998) Adaptive control[M]. Springer, New York

    Google Scholar 

  10. 10.

    Kamal S, Bandyopadhyay B (2015) High performance regulator for fractional order systems: a soft variable structure control approach[J]. Asian J Control 17(4):1342–1346

    MathSciNet  Article  Google Scholar 

  11. 11.

    Kim E, Lee S (2005) Output feedback tracking control of MIMO systems using a fuzzy disturbance observer and its application to the speed control of a PM synchronous motor[J]. IEEE Trans Fuzzy Syst 13(6):725–741

    Article  Google Scholar 

  12. 12.

    Pano-Azucena AD, Tlelo-Cuautle E, Muñoz-Pacheco JM, de la Fraga LG (2019) FPGA-based implementation of different families of fractional-order chaotic oscillators applying Grünwald-Letnikov method. Commun Nonlinear Sci Numer Simul 72:516–527

    MathSciNet  Article  Google Scholar 

  13. 13.

    Aghababa MP (2012) Robust stabilization and synchronization of a class of fractional-order chaotic systems via a novel fractional sliding mode controller[J]. Commun Nonlinear Sci Numer Simul 17(6):2670–2681

    MathSciNet  Article  Google Scholar 

  14. 14.

    Aghababa MP (2012) Finite-time chaos control and synchronization of fractional-order nonautonomous chaotic (hyperchaotic) systems using fractional nonsingular terminal sliding mode technique[J]. Nonlinear Dyn 69(1–2):247–261

    MathSciNet  Article  Google Scholar 

  15. 15.

    Yang J, Chen WH, Li S (2011) Non-linear disturbance observer-based robust control for systems with mismatched disturbances/uncertainties[J]. IET Control Theory Appl 5(18):2053–2062

    MathSciNet  Article  Google Scholar 

  16. 16.

    Ellis G (2002) Observers in control systems: a practical guide[M]. Elsevier, Amsterdam

    Google Scholar 

  17. 17.

    Rajamani R (1998) Observers for Lipschitz nonlinear systems[J]. IEEE Trans Autom Control 43(3):397–401

    MathSciNet  Article  Google Scholar 

  18. 18.

    Chen M, Chen WH (2010) Sliding mode control for a class of uncertain nonlinear system based on disturbance observer[J]. Int J Adapt Control Signal Process 24(1):51–64

    MathSciNet  MATH  Google Scholar 

  19. 19.

    Sastry SS, Isidori A (1989) Adaptive control of linearizable systems[J]. IEEE Trans Autom Control 34(11):1123–1131

    MathSciNet  Article  Google Scholar 

  20. 20.

    Chen L, Narendra KS (2001) Nonlinear adaptive control using neural networks and multiple models[J]. Automatica 37(8):1245–1255

    MathSciNet  Article  Google Scholar 

  21. 21.

    Mishra S (2006) Neural-network-based adaptive UPFC for improving transient stability performance of power system[J]. IEEE Trans Neural Netw 17(2):461–470

    Article  Google Scholar 

  22. 22.

    Warwick K (1995) A critique of neural networks for discrete-time linear control[J]. Int J Control 61(6):1253–1264

    MathSciNet  Article  Google Scholar 

  23. 23.

    Pecora LM, Carroll TL (1991) Driving systems with chaotic signals[J]. Phys Rev A 44(4):2374

    Article  Google Scholar 

  24. 24.

    Stamova I (2014) Global Mittag-Leffler stability and synchronization of impulsive fractional-order neural networks with time-varying delays[J]. Nonlinear Dyn 77(4):1251–1260

    MathSciNet  Article  Google Scholar 

  25. 25.

    Podlubny I (1998) Fractional differential equations: an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications[M]. Elsevier, Amsterdam

    Google Scholar 

  26. 26.

    Diethelm K (2010) The analysis of fractional differential equations: an application-oriented exposition using differential operators of Caputo type[M]. Springer, Berlin

    Google Scholar 

  27. 27.

    Chen M, Ge SS, How BVE (2010) Robust adaptive neural network control for a class of uncertain MIMO nonlinear systems with input nonlinearities[J]. IEEE Trans Neural Netw 21(5):796–812

    Article  Google Scholar 

  28. 28.

    Hardy GH, Littlewood JE, Pólya G et al (1952) Inequalities[M]. Cambridge University Press, Cambridge

    Google Scholar 

  29. 29.

    Shao S, Chen M, Chen S et al (2016) Adaptive neural control for an uncertain fractional-order rotational mechanical system using disturbance observer[J]. IET Control Theory Appl 10(16):1972–1980

    MathSciNet  Article  Google Scholar 

  30. 30.

    Khanzadeh A, Pourgholi M (2016) A novel continuous time-varying sliding mode controller for robustly synchronizing non-identical fractional-order chaotic systems precisely at any arbitrary pre-specified time[J]. Nonlinear Dyn 86(1):543–558

    MathSciNet  Article  Google Scholar 

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Correspondence to Zihui Xu.

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Shao, K., Xu, Z. & Wang, T. Robust finite-time sliding mode synchronization of fractional-order hyper-chaotic systems based on adaptive neural network and disturbances observer. Int. J. Dynam. Control (2020). https://doi.org/10.1007/s40435-020-00657-4

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Keywords

  • Fractional hyper-chaotic system
  • Adaptive sliding mode law
  • Adaptive neural network
  • Disturbance observer